rtvvar {ssaBSS}

Simulation of Time Series with Time-varying Variance

Description

Simulating time-varying variance based on TV-VAR model

Usage

rtvvar(n, alpha, beta = 1, simple = FALSE)

Arguments

n

Length of the time series

alpha

Parameter \alpha in TV-VAR

beta

Parameter \beta in TV-VAR. Default is 1.

simple

A logical vector indicating whether h_t is considered as its own process, or just t/T. Default is FALSE.

Details

Time varying variance (TV-VAR) process x_t with parameters \alpha and \beta is of the form

x_t = \tilde h_t \epsilon_t,

where, if simple = FALSE,

\tilde h_t^2 = h_t^2 + \alpha x_{t-1}^2,

where \epsilon are iid N(0,1), x_0 = 0 and h_t = 10 - 10 \sin(\beta \pi t/T + \pi/6) (1 + t/T),

and if simple = TRUE,

\tilde h_t = t/T.

Value

The simulated series as a ts object.

Author(s)

Sara Taskinen, Markus Matilainen

References

Patilea V. and Raïssi H. (2014) Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance, Journal of the American Statistical Association, 109 (507), 1099-1111.

Examples

n <- 5000
X <- rtvvar(n, alpha = 0.2, beta = 0.5, simple = FALSE)
plot(X)